The 2006 print, one of 33 from Banksy's LA Edition, was passed to auctioneers Lyon & Turnbull by a friend of the artist.
With a cheeky nod to the Fringe, the screen-print is named Festival and shows punters lining up to buy "Destroy capitalism" T-shirts for $30.
Auction house specialist Ben Hanly said the work was different to the type the firm usually handles.
"It is classic Banksy at his best, and this print is quite rare," he said. "It's meant to be a fun thing and he is a sought-after artist.
"We have sold 15 or 20 works by him in London, but never in Edinburgh. We think there's a national interest in what he's doing."
The print is expected to fetch between 3,000 and 5,000 but similar prints in galleries have sold for more than 7,000.
The largest sum ever paid for a Banksy piece was 102,000, for anti-war print Bombing Middle England in 2007.
The sale will take place at 11am on 28 April, at the Lyon & Turnbull saleroom in Broughton Place.